It's tough when you really want some nice home-grown tomatoes. But to do the best with what you have, use tomatoes known to do better in shade than others. I won't try to toss out all the names, because there are different names offered by different sources. But you can search the Internet for "shade tomatoes" and look for some of the suggestions. Cherry tomatoes are popular with shade gardeners because they take such little time to mature. Five hours of sun can be adequate for them. Two readily available ones are Sweet 100 and Yellow Pear.
If you have choices, it sounds like you just have to pick the best spot. If both a morning and an evening location have equal hours of sun, pick the morning spot. It will also be a bit cooler there, and tomatoes aren't fond of heat and can stop flowering and setting fruit in high heat. (Although it's not the absolute killer is often sounds.) That may be part of your tomato experience too, since you're in Florida. That Sweet 100 I mentioned is one of many modern relatively heat-tolerant varieties. Names with "Sun" and other "heat" words are usually heat-tolerant.
In our situations, shade is not always evil. I don't think you are likely to need artificial shade, but here's a little dissertation the help make you feel better after all that talk about sun:
http://www.tomatodirt.com/too-...
I keep that site bookmarked, because of all the information in an accessible form.
I'm working right now on a Dutch pot hydroponic set-up with insulated reservoir and pots and ice-cooled nutrient solution, because I can't grow in the air conditioning, and here in a Texas summer, it's as hot on a porch or greenhouse as outdoors. I also have some questions about tomato plants controlling their own temperature when they have plenty of water readily available and will using a probe to track that. There is scientific evidence that they do, and I see people growing hydroponically and successfully in high heat. If you want to explore that in a simple and non-labor-intensive way, take a look at Kratky hydroponics.
https://youtu.be/LQQlHnQ7fPU